1. Field of the Invention
The present invention relates to a process simulation of ion implantation that is used in the semiconductor device manufacturing process. More particularly, the present invention relates, for example, to the simulation of an ion density distribution in an ion implantation process.
2. Description of the Related Art
The process simulation of ion implantation is classified broadly into the Monte Carlo method and the distribution function method. The distribution function method, also called analytic method, approximates an ion distribution by an analytic function. With the distribution function method, there is a high demand for conflicting requirements of shorter computing time and accuracy improvement. This demand has been answered, for example, by a conventional technique disclosed in Japanese Patent Unexamined Publication No. 2000-340518 (Patent Literature 1) of a semiconductor process simulation method outlined below. The semiconductor process simulation method is directed to a simulation based on the discrete computation of the impurity density of a semiconductor device structure. The semiconductor process simulation method is characterized by presetting the position of a grid required for the discreet computation based on simulation procedure data. The grid position presetting method includes adding more grids, in addition to an initial grid, at the position of a maximum value of the impurity distribution function by an ion implantation. Still, more grids are added further until the ion implantation simulation reaches an error range desired.
With the accuracy improvement of the ion implantation simulation based on a distribution function method, beam dispersion of an ion beam implanted has become an indispensable consideration. More specifically, if a semiconductor device is miniaturized, then the temperature of the thermal process will become low, the time will become shorter, so that the distribution of impurity implanted through ion implantation into a device is inhibited. This means that it is the impurity distribution adopted in the ion implantation process that controls the device characteristics. For this reason, in addition to the effects on the device characteristics of the energy and the implantation angle that characterize the density distribution of impurity within a device through ion implantation, the effects on the device characteristics of the angular distribution of an ion beam implanted (also called ion beam dispersion or beam dispersion), which had received little attention, have also become noticeable.
In addition, if a semiconductor device is miniaturized and consequently the implantation energy is lowered, then the self-reaction of an ion becomes noticeable, and the beam dispersion itself has become large. If beam dispersion occurs in a field-effect transistor, for example, then the amount of ion that is implanted into a silicon substrate is reduced by the effects of a “shadow” caused by a gate electrode. This may lead to a reduction in driving force for the transistor. Therefore, the ion implantation simulation requires a highly accurate computation of the effects of the “shadow” caused by the gate electrode so that such a phenomenon can be predicted.
Conventional ion implantation simulators that use the distribution function, however, have no function to perform a directly execution of a simulation involving beam dispersion. If a simulation involving the beam dispersion is performed by an angular integration of an implantation angle based on a conventional simulation method, then the computing time will increase, which is a problem. The problem of increased computing time is vital in three-dimensional simulation. A brief description of those problems will be given below.
FIG. 13 is a diagram illustrating a conventional computation of ion implantation with no consideration of the beam dispersion. To ensure precision in computation near a device edge of a device area, extended areas as areas to be used for the computation of ion implantation are set so as to extend the device area on both sides. With the conventional computation of ion implantation with no consideration of beam dispersion, a computation area will hereinafter be referred to as an extended device area, if not otherwise specified. With the conventional computation of ion implantation with no consideration of beam dispersion, a formula 1 shown in FIG. 14, for example, is used as the distribution function of an ion. With reference to the formula, V(rp) denotes a vertical distribution function, e.g., Pearson function; H(rl) denotes a horizontal distribution function, e.g., a Gauss function; and D denotes a doze amount. FIG. 15 is a diagram illustrating the case where the device of the diagram of FIG. 14 receives ion beams implanted. The ion density at an arbitrary point C (xo, yo) in an area 2 is obtained by a formula 2 shown in FIG. 15. In other words, an ion implantation distribution can be obtained by integrating the distribution function in the horizontal direction (towards the x direction).
A description will now be given, with reference to FIG. 16, of the computation method of ion implantation that involves the beam dispersion by an angular integration of the implantation angle based on the conventional simulation method. According to this method, ion density at the arbitrary point C (xo, yo) in the area 2 is obtained by a direct angular integration (Double Integral) base on a formula 3 shown in FIG. 16. With reference to the formula 3, G(θ) denotes the beam dispersion, which is approximated by the Gauss function of a formula 4, θ0 denotes the implantation angle, and σ0 denotes the angular distribution.
[Patent Literature 1] Unexamined Patent Publication No. 2000-340518.